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NDA2022MathematicsDifferential EquationsActual

What is the differential equation of the family of parabolas having vertex at origin and axis along positive y -axis ?

Options

  1. Ax d y d x +2 y=0
  2. Bx d y d x -2 y=0
  3. Cy d x d y +2 x=0
  4. Dy d x d y -2 x=0

Correct answer

B. x d y d x -2 y=0

Step-by-step solution

Let equation of parabola is x^2=4 a y ...(i) aligned & 2 x=4 a d y d x & 2 x= x^2 y d y d x x d y d x -2 y=0 aligned

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